Charmed Mesons Have No Discernable Color-Coulomb Attraction

TL;DR

This paper demonstrates through relativistic quark model calculations that charmed mesons do not exhibit a discernible color-Coulomb attraction, with the effective potential remaining essentially linear.

Contribution

It shows that the color-Coulomb attraction effectively disappears in charmed mesons, challenging the necessity of including such attraction in quark potential models.

Findings

Coulomb attraction mostly disappears after convolution with quark densities.

Effective potentials remain essentially linear for c- and u-quarks.

Charmed-meson mass spectrum can be described without color-Coulomb attraction.

Abstract

Starting with a confining linear Lorentz scalar potential V_s and a Lorentz vector potential V_v which is also linear but has in addition a color-Coulomb attraction piece, -alpha_s/r, we solve the Dirac equation for the ground-state c- and u-quark wave functions. Then, convolving V_v with the u-quark density, we find that the Coulomb attraction mostly disappears, making an essentially linear barV_v for the c-quark. A similar convolution using the c-quark density also leads to an essentially linear tildeV_v for the u-quark. For bound cbar-c charmonia, where one must solve using a reduced mass for the c-quarks, we also find an essentially linear widehatV_v. Thus, the relativistic quark model describes how the charmed-meson mass spectrum avoids the need for a color-Coulomb attraction.